Induction Motor's Speed at Maximum Torque

[Michael Neo]

Homework Statement

A two-pole, wound rotor, induction motor has a rotor resistance of 0.8 ohms per phase and a rotor leakage reactance of 7 ohms.

At what speed will the motor produce maximum torque when fed from a 50 Hz supply?

Relevant Equations

Torque is maximum when R2=sX2

For maximum torque, X2=R2/s

Therefore, s=R2/X2

Synchronous speed, ns=F*60/p (rev min-1)

Maximum Slip

s=4/35

Synchronous Speed

n_s=50*60/p

n_s=3000 rev min^-1

Speed at Maximum Torque

Torque is maximum when R₂=sX₂

For maximum torque, X₂=R₂/s

I'm not sure after this.

 

[Michael Neo]

Speed at Maximum Torque

n_s*(1-s)

(3000)*(1-0.1142857143)
(3000)*(0.8857142857)

=2657.142857 rev min^-1

 

[hutchphd]

What is p ?

 

[Michael Neo]

p=number of pole pairs

There are two poles.

Therefore, p=1

 

[hutchphd]

Number of pairs...thanks. As a former engineering prof, I would also ask why you think it necessary to report 9 significant figures in your calculations, but that is a different discussion...

 

[Michael Neo]

The number of significant figures or decimal places required is not specified.

 

[hutchphd]

Understood...but I have found it useful always to only worry about the significant parts of every problem...consider it a small mental discipline so you don't "miss the forest for the trees".

 

[Michael Neo]

If maximum torque occurs when R₂ = sX₂, what resistance must be added to the rotor circuit to give maximum starting torque?

s=1 at standstill.
X₂=7 at standstill.
R₂=0.8 at standstill.

If maximum torque occurs when R₂=sX₂

Then, at standstill,
R₂=(1)X₂

Therefore,
R₂=X₂

Resistance added to give maximum starting torque

At standstill, the maximum starting torque occurs when,
R₂=X₂

However, not equal,
R₂=0.8
X₂=7

Therefore, calculate what must be added to make them equal.

0.8 + 6.2 = 7

Therefore,

6.2 Ohms must be added to make them equal and, therefore, give the maximum starting torque.

 

[Tom.G]

6.2 Ohms must be added to make them equal and, therefore, give the maximum starting torque.

I find that statement a bit unclear. Can someone clarify?
Is it 1., 2., or both?

1. The maximum torque the motor can supply occurs at start-up
2. This maximizes the torque available at start-up

 

[Michael Neo]

I interpreted the question to mean the maximum torque available at start-up. So, statement 2.

I used the phrase in the question "...give maximum starting torque" to avoid ambiguity and used the phrase "...to make them equal" to help anyone else with a similar question understand.

This might be clearer:

6.2 Ohms resistance must be added to the rotor circuit to give maximum starting torque.

Again, I've used the phrase used in the question, but nothing else.

 

[Babadag]

The maximum torque value does not depend on rotor resistance then if you add 6.2 ohm to rotor resistance the maximum torque will remain unchanged but the point in where this maximum occurs [the slip s] will change. If you will add 6.2 ohm this point will be at s=1 [at starting point].